1. Field of the Invention
The present invention relates generally to a method for solving stochastic control problems of linear systems in high dimensions.
2. Description of Related Art
(Note: This application references a number of different publications as indicated throughout the specification by reference numbers enclosed in brackets, e.g., [x]. A list of these different publications ordered according to these reference numbers can be found in the Section entitled “References” in the “Detailed Description of the Preferred Embodiment.” Each of these publications is incorporated by reference herein.)
Computer-implemented Supply Chain Management (SCM) applications are designed to link a cohesive production and distribution network and thus allow an enterprise to track and streamline the flow of materials and data through the process of manufacturing and distribution to customers. SCM applications represent a significant evolution from previous enterprise resource planning (ERP) systems
One goal of SCM applications is to decrease inventory costs by matching production to demand. SCM applications utilize extremely complex forecasting and planning algorithms to predict demand based upon information stored in the enterprise's database. These applications also incorporate any changes in supply chain data into the forecast much faster than previous modes of calculation, allowing enterprises to more accurately predict demand patterns and schedule production accordingly.
Another goal of SCM applications is to reduce overall production costs by streamlining the flow of goods through the production process and improving information flow between the enterprise, its suppliers, and its distributors. Logistics-oriented systems, such as transportation, warehouse management, and factory scheduling applications, all contribute to reduced production costs. By ensuring real-time connectivity between the various parties in a supply chain, these applications decrease idle time, reduce the need to store inventory, and prevent bottlenecks in the production process.
Yet another goal of SCM applications is to improve customer satisfaction by offering increased speed and adaptability. SCM applications allow the enterprise to reduce lead times, increase quality, and offer greater customization, enhancing the customer relationship and improving retention.
SCM applications begin with forecasting and data mining applications analyzing information consolidated in the enterprise's database. Planning algorithms are used to generate a demand forecast upon which to base subsequent procurement orders and production schedules.
Nonetheless, there is a need in the art for improved planning techniques for SCM applications, especially where a SCM application models a Markov Decision Process (MDP), and the action space and the state space of the MDP model are continuous and related to each other through a system of linear constraints.